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We present an analysis of the dense gas structures in the immediatesurroundings of the massive young stellar object (MYSO) W42-MME, using thehigh-resolution (0$''$.31$\times$0$''$.25) ALMA dust continuum and molecularline data. We performed a dendrogram analysis of H$^{13}$CO$^{+}$ (4-3) linedata to study multi-scale structures and their spatio-kinematic properties, andanalyzed the fragmentation and dynamics of dense structures down to $\sim$2000AU scale. Our results reveal 19 dense gas structures, out of which 12 areleaves and 7 are branches in dendrogram terminology. These structures exhibittransonic-supersonic gas motions (1$<\mathcal{M}<5$) with overvirial states($\alpha_{\rm vir}\geq2$). The non-thermal velocity dispersion-size relation($\sigma_{\rm nt}-L$) of dendrogram structures shows a weak negativecorrelation, while the velocity dispersion across the sky($\delta\mathit{V_{\rm lsr}}$) correlates positively with structure size ($L$).Velocity structure function ($S_{2}(l)^{1/2}$) analysis of H$^{13}$CO$^{+}$data reveals strong power-law dependencies with lag ($l$) up to a scale lengthof $\lesssim$ 6000 AU. The mass-size ($M-R$) relation of dendrogram structuresshows a positive correlation with power-law index of 1.73$\pm$0.23, and theleaf L17 hosting W42-MME meets the mass-size conditions for massive starformation. Blue asymmetry is observed in the H$^{12}$CO$^{+}$ (4-3) lineprofiles of most of the leaves, indicating infall. Overall, our resultsobservationally support the hierarchical and chaotic collapse scenario in theproximity of the MYSO W42-MME.

Fragmentation and dynamics of dense gas structures in the proximity of massive young stellar object W42-MME